Denis Zakaria’s early own goal had put the three-time champions ahead but Xherdan Shaqiri made it 1-1 midway through the second half.
After Remo Freuler’s harsh red card for the Swiss Spain, who missed a host of chances in extra time, prevailed 3-1 on spot-kicks.
“In terms of the penalties I was calm as it wasn’t down to me,” Enrique said.
“Once the players had decided who was going to take them we all had huge faith in Unai and the takers so all you could do was wait to see.
“I told them to enjoy the moment as much as they could. We didn’t get off to a good start [Sergio Busquets hit the post] but the players were able to turn it around.
“People say it is a lottery but it isn’t at all, everything comes into it: the ability to deal with pressure, the goalkeepers, but when it goes your way it feels very good indeed.”
Asked if he had told Simon he could be a hero Enrique added: “Any coach thinks that when they speak to their goalkeeper.
“I’ve seen him save many penalties for Athletic [Bilbao]. I tried to tell him to put pressure on the taker but I was completely relaxed and had faith whatever happened.”
Enrique said he always considered his side to be contenders but now they were in the last four they had to start thinking about a fourth title.
“I’ve always said we were one of the eight teams who had a chance of winning the title but it was dependent on our performances,” he added.
“Now we are in the last four that is fantastic and fills us with a great sense of pride.
“It would be ridiculous to think the four semi-finalists aren’t going to be thinking about going one further and go to the the final.”
Switzerland’s captain on the night Shaqiri told euro2020.com: “I’m really proud of the team. Penalties are a bit 50-50.
“I was nervous watching the shoot-out. I think we just lacked a little bit of luck today.”
Coach Vladimir Petkovic had mixed emotions after their exit from the tournament.
“I am very proud of my team and the players. Unfortunately a red card like this affected our game for 45 minutes but all these players were the heroes of the night,” he said.
“We would have deserved to get to the semi-finals but unfortunately we were tired.
“I cannot complain about anything and I take my hat off to the team.”
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in